Preheat the oven to 325°F.
In a medium bowl, combine graham cracker crumbs, melted butter, and 1/4 cup granulated sugar. Mix until well combined.
Press the mixture firmly into the bottom of a 9-inch springform pan to form the crust. Bake for 10 minutes, then remove from the oven and let cool.
In a large mixing bowl, beat the softened cream cheese with 1 cup granulated sugar and vanilla extract until smooth and creamy.
Add the eggs one at a time, mixing well after each addition. Stir in the sour cream until fully incorporated.
In a separate bowl, toss the sliced peaches with brown sugar and cinnamon until evenly coated.
Pour half of the cheesecake batter over the cooled crust, then layer half of the peach mixture on top.
Pour the remaining cheesecake batter over the peaches, followed by the rest of the peach mixture.
Bake in the preheated oven for 50-60 minutes, or until the center is set and the edges are lightly golden.
Turn off the oven and leave the cheesecake inside for an additional hour to cool gradually.
Once cooled, refrigerate for at least 4 hours or overnight before serving.